415 words - 2 pages

Time Series Analysis

Yt=observed value of the time series in time period t

TRt=the trend component or factorin time period t

SNt=the seasonal componentor factorin time period t

CLt=the cyclical componentor factorin time period t

IRt=the irregular componentor factorin time period t

7.1)

CL*IRCL=IR

a) SN1=1.191

TR1=240.5

CL1=null

IRt=null

SN2=1.521

TR2=260.4

CL2=0.998

IR2=0.990

SN3=0.804

TR3=280.4

CL3=0.994

IR3=0.986

SN4=0.484

TR4=300.3

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53+19.94(t)

c) Yt=trt*snt

Y17=220.53+19.9417*1.191=666.6

Y18=220.53+19.9418*1.521=881.6

Y19=220.53+19.9419*0.804=482.1

Y20=220.53+19.9420*0.484=299.9

d)

Yt=trt*snt*cl

We cannot see a definitive cycle and because the values of cl are close to 1. We do not take it into account.

Y21=220.53+19.9421*0.191=761.6

e)

Since there are just four years of data and most values are near 1 we cannot discern a well-defined cycle.

f)

Y21=220.53+19.9421*0.191=761.6

It agrees with the values computed in part c

g) Excel Spreadsheet

h)

Prediction intervals for the next 4 quarters t=17,18,19,20

t=17:654.094,679.542

t=18:869.038,894.542

t=19:469.107,494.556

t=20:286.977,312.426

8.1)

Smoothing equation

l0=t=1nYtn Which is the average of the first series values

lT=αyT+(1-α)lT-1

α:smoothing constant

Yt+1=lt

a)

l0=360.66

l1=0.1362+0.9360.66=360.80

l2=0.1381+0.9360.80=362.82

l3=0.1317+0.9362.82=358.23

b)

l4=0.1297+0.9358.23=352.11

Forecast error for τ=4: 297-358.23=-61.23

c)

l4=0.1297+0.9358.23=352.11

d)

Forecast error for τ=5: 399-352.11=46.89

8.3)

a)

PI Y28=354.54±1.9634.951+30.034=[282.62,426.45]

b)

YT+τT=lT

Y24+524=l24=348.63

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